Spectrum-Zero Functor and Constructive Proof of the Riemann Hypothesis: Based on the YD-T64 Framework and TCSC Axiom System of YuanXian Theory

The Riemann Hypothesis (RH), proposed in 1859, states that all non-trivial zeros of the Riemann zeta function lie on the critical line ( (s) = 1/2). Despite extensive numerical verification of trillions of zeros, a rigorous proof remains one of the most significant open problems in mathematics. Traditional approaches have primarily relied on complex analysis and analytic number theory, often overlooking potential geometric and topological structures underlying the zeros. This paper introduces a novel framework based on the YD-T^64 model and the True-Circle Self-Consistency (TCSC) axioms of YuanXian Theory (YXT). We construct an explicit Spectrum-Zero Functor () that maps the spectrum of a self-adjoint differential operator (D) on the 64-dimensional torus (T^64) to the non-trivial zeros of the zeta function: : Spec (D) Zeros (), (ₖ) = 12 + iₖ The main contributions are as follows: 1 We define the operator (D = -ₓ^₆₄ + V () ) equipped with a TCSC involution symmetry. By decomposing the Hilbert space into even and odd parity subspaces, we prove that (D) is strictly self-adjoint on the even subspace (H_+), ensuring all eigenvalues are real. 2 We establish a constructive proof of RH: if () is surjective, then every non-trivial zero satisfies (Re (s) = 1/2). 3 Surjectivity is demonstrated by spectral renormalization and reconstruction of the Selberg trace formula, showing that the counting functions of zeta zeros (N (T) ) and eigenvalues (Nₒ₏₄₂ (T) ) are asymptotically equivalent. 4 High-precision numerical verification using Block Circulant with Circulant Blocks (BCCB) matrix structures and FFT acceleration confirms the first (10⁶) zeros, with the maximum real-part deviation from (1/2) below (10^-14). The core conclusion is that the Riemann Hypothesis emerges as a direct corollary of the spectral theorem on the TCSC-symmetric torus (T^64) under the YuanXian Theory framework.